We report the fabrication of a novel type of hollow core photonic bandgap fiber (PBGF) with a small core formed by 3 omitted unit cells in a triangular array of holes. The transmission properties of fibers designed for operation at 1500nm wavelength are investigated both experimentally and through extensive modeling. The novel PBGF structure provides robust single mode guidance and is of particular interest for device applications which require low index bandgap guidance and short device lengths.
©2008 Optical Society of America
Photonic bandgap fibers (PBGFs) exploit a radically different mechanism as compared to conventional index-guiding fibers, enabling light guidance in a low refractive index core surrounded by a photonic crystal cladding. Low-loss diffractionless propagation of optical modes can take place in hollow core PBGFs over distances well beyond the free-space Rayleigh limit . These fibers exhibit a host of novel and unusual transmission properties, which has prompted strong interest in recent years. The low overlap between the guided light and glass structure, which correlates with high optical damage thresholds and very low nonlinearity, the wide-ranging values of dispersion that are found in PBGFs, and the ability to obtain long interaction lengths with gas or liquid formulations in-diffused in the hollow core have allowed important advances in applications areas such as high power delivery , pulse compression , chemical sensing  and gas-based nonlinear optics , amongst others.
Hollow core PBGFs rely on a 2-D photonic crystal formed by an array of air holes, which are generally arranged on a triangular lattice and present as high as 90% air filling factor. Guidance is obtained via coherent Bragg scattering where light at wavelengths within well-defined stop bands is prohibited from propagating in the photonic crystal cladding and is therefore confined to a central defect. Very tight tolerances on the structural parameters and high consistency along the fiber length are paramount for PBGFs, and considerable refinements of the stack-and-draw fabrication technique have been necessary in order to obtain low loss fibers . The hollow core is formed by an oversized air hole, which is produced by omitting a number of elements in the middle of a stack of capillaries; due to this fabrication constraint, the core diameter is generally found to be approximately equal to a multiple of the lattice constant of the photonic crystal cladding.
The two most commonly employed PBGF structures have a core formed by either 7 or 19 omitted cells, which we will designate 7c and 19c, respectively. It is well established [6, 7] that both these structures can support a number of optical modes at any given wavelength within the bandgap. These include both air-guided modes, i.e. modes in which most of the optical power is located in the hollow core, and modes in which the optical power is located in the thin silica strands at the core boundary or in its close proximity. The latter are commonly termed surface modes (SMs), and their interaction with the air guided modes introduces an important loss mechanism for PBGFs [8, 9]. The type and number of modes supported by a PBGF is determined by the size and shape of the core and that of its glass boundary. For instance, recent studies [10, 11] have revealed that the number of SMs and their wavelength position relative to the centre of the bandgap is largely determined by the thickness of the silica ring which defines the core boundary. If the latter equals approximately half the thickness of the glass strands forming the photonic crystal cladding, SMs are effectively suppressed in an idealized structure and furthermore this holds true for both 7c and 19c structures [10, 12]. On the other hand, the number of air guided modes supported by a PBGF is determined, to the first order, by the core dimension, i.e. it scales approximately linearly with the area of the core [7, 13] according to the following equation:
where NMAX is the maximum number of modes within the range of frequencies of the bandgap, (which occurs at the frequency ω0 defined by the intersection of the light line, β=k, with the long-wavelength edge of the bandgap ), kL(ω) is the wave vector at the lower frequency edge of the bandgap, R C is the core radius and Λ is the hole to hole spacing of the photonic crystal cladding. By assuming a typical choice of values for kL(ω) and ω0 (which depend on the structure of the cladding), it results from Eq. (1) that a 7c PBGF, which has Rc≈1.5·Λ, supports 10 to 14 optical modes, whereas a 19c PBGF, with Rc≈2.5·Λ, is expected to have 35 to 45 modes. Equation (1) also provides a rough indication of the maximum core radius compatible with strictly single mode operation; again in the most common cladding design regimes, such condition is met by structures having a core diameter only slightly larger than the hole-to-hole spacing (Rc≈0.6·Λ). Strategies to achieve single mode guidance through a reduction in the core size have been proposed and investigated numerically [14, 15]. Reference , in particular, introduces a PBGF structure with a 3 cell core, demonstrating a lower number of supported modes as compared to the 7c (only 6 modes) and effective single mode guidance.
For most applications reported to date, the multi-moded nature of the 7c or 19c PBGFs does not represent a significant drawback [6, 7]. The fundamental mode can be selectively excited by careful design of the launch optics. Furthermore, because the higher order modes have in general higher confinement and scattering losses as compared to the fundamental mode, it is often possible to exploit such differential loss in order to obtain an effectively single mode output at the desired wavelength, provided a sufficiently long length of fiber can be employed. However, any fluctuation in the launch conditions, as well as intermodal coupling due to local structural variations along the fiber, may result in a fraction of power being transferred from the fundamental to higher order modes. This fraction has been quantified as a few percent in a 7c PBGF, under optimized launch conditions and after propagation through a 50m length of fiber . In general, when higher order modal content is present, the properties of the transmitted beam become dependent on the relative phase of all the modes, and these are prone to change with time due to bends and any other externally applied perturbations, including environmental factors. It is important to point out that the presence of higher order modes in PBGFs cannot be readily identified from mode quality factor (M2) measurements, as is commonly done in most conventional fibers, because of the non-Gaussian nature of the air guided modes in these structures .
Several applications of hollow core PBGFs can be envisaged which may require, or would gain a definite benefit from, single mode propagation through a short length of fiber. Possible examples include: high power laser delivery, where higher order modes may lead to non-uniform or time-dependent output intensity distributions; PBGFs filled with optically active (gas or liquid) media for fiber lasers or Raman converters, where coupling the pump wavelength into higher order modes may lead to reduced efficiency ; and interferometric or grating based sensing, where higher order modes may lead to distorted patterns or extra reflection peaks, respectively. In addition, the control of phase noise and other issues arising from a small percentage of power guided through high order modes may also prove beneficial for some applications employing long lengths of fiber, such as in data transmission and in the fiber gyroscope , provided a sufficiently low fiber loss can be achieved.
In this study we report, for the first time to our knowledge, the fabrication of a 3c hollow core PBGF showing low loss guidance and strictly single mode operation. We perform a detailed numerical and experimental investigation of its transmission properties and compare it to those of the more conventional 7c and 19c PBGF structures.
2. Single mode PBGF and its characterization
A scanning electron microscope (SEM) image of the cross section of the 3c PBGF is shown in Fig. 1. The fiber was fabricated using a conventional stack-and-draw technique. A preform was assembled by stacking a few hundred highly-uniform, thin-walled capillaries made of high purity synthetic silica glass, with three elements removed from the centre of the array to form the core. The stack was then inserted in a silica jacketing tube, and was drawn into a millimeter sized cane first and subsequently into a fiber via a rod-in-tube technique. Suitable pressure differentials were applied during the two drawing steps in order to achieve the required scale factor while maintaining a structure with an overall high air filling factor.
Figure 2 (top row) shows SEM micrographs of the core region of the 3c PBGF, together with more conventional 7c and 19c PBGF structures, which were fabricated using the same technique in order to compare their optical properties. All fibers incorporate a periodic cladding with seven complete rings of holes, plus a further eighth incomplete ring (visible in Fig. 1 for the 3c PBGF), which was added in order to minimize the deformation of the photonic crystal cladding during the fiber draw due to the shape mismatch between the triangular stack and the outer cylindrical jacketing tube. The cladding is characterized by the hole-to-hole spacing, Λ, by the relative hole size, d/Λ, and by the hole shape factor, dC/d, which defines the degree of hexagonal distortion of the holes observed in high air-filling factor structures . These parameters are all very close for the three fibers and are optimized for operation around 1500nm. The core boundary thickness was carefully chosen to adhere to the design regimes identified in reference  in order to minimize the incidence of SM anticrossings with the fundamental mode at wavelengths inside the bandgap. Analysis of the SEM images of the three fibers gave a value of Λ≈3.6–3.9µm for the average hole-to-hole spacing, d/Λ≈0.97 for the average relative hole diameter, and the hexagonal holes were rounded with circular sectors of diameter dC/d≈0.4. The corresponding air filling factor was approximately 93%. The measured core diameters were 9, 12 and 20µm for the 3c, 7c and 19c PBGFs, respectively.
We calculated the optical properties of these fibers by performing detailed modal simulations using a full vector finite element method [21, 22]. A selected set of results is shown in Fig. 3. The structural parameters measured in our real fibers were used as input for the calculations. The idealized cross section used for the three fibers is shown in Fig. 2 (bottom row). The main difference between real and ideal structures lies in the first ring of holes, where the real fibers present a slightly more rounded profile of the core boundary. The calculated bandgap is delimited by a gray line in Fig. 3 (top row) and it extends, along the air line (β=k), between ≈1300 and ≈1560 nm. The top row of graphs in Fig. 3 also shows the effective index (neff) of each air-guided mode supported by the three structures as a function of the wavelength. Remarkably, in the 3c PBGF, only two degenerate LP01-like modes are found at each wavelength inside the bandgap. In contrast, the 7c PBGF supports up to 12 modes for the same choice of cladding parameters (LP01, LP11, LP02 and LP21-like), while up to 40 modes can exist in the 19c PBGF at wavelengths around 1570 nm. It is important to note that none of the idealized structures present an anticrossing between the fundamental mode and a surface mode within the bandgap, which is a consequence of the core ring thickness satisfying the constraints of the design regime identified in reference . This supports the claim that such a design regime is of general validity for PBGF structures based on a triangular lattice of holes, irrespective of their core shape. The intensity profiles of the fundamental air guided modes calculated for the 3c, 7c and 19c PBGFs are superimposed on the idealized structures in Fig. 2 (bottom row).
For all the air guided modes supported by each of the three fibers we also calculated the percentage of power in the hollow core, the percentage of power in the glass, the effective area (Aeff), the nonlinear coefficient (γ), the confinement loss (CL) and the surface scattering coefficient (commonly termed F-factor), which is proportional to the integral of the squared norm of the electric field along the glass-air boundaries . A summary of these results for the respective fundamental modes of the three fibers is shown in Table 1: the first three columns show the spread of values across the full optical bandgap, while the second three columns give the value at the central wavelength (1500nm).
We observe that the optical properties of the 3c PBGF present more pronounced wavelength dependence than the other two fibers. The reason for this can be inferred from the effective index versus wavelength plots in Fig. 3 (top row). Contrary to the 7c and 19c PBGFs, where the effective index varies very little within the bandgap and terminates abruptly at its edges, the effective index in the 3c PBGF has a smoother transition at the long wavelength edge; in this region, the neff decreases significantly, which can be interpreted in a ray optics picture as a gradual decrease of the mode’s angle of incidence with respect to the core boundary. In addition, the amount of power in the core decreases, while Aeff, CL and F all increase with wavelength - leading to a more substantial distribution of values across the bandgap, as compared to 7c and 19c structures. Due to its smaller core radius, the percentage of power in the glass at 1500nm is ~3% for the 3c PBGF, as compared to <1% and <0.5% for 7c and 19c PBGFs, respectively. While this is likely to reduce the damage threshold for these fibers, it also results in an increased nonlinear coefficient of the 3c PBGF, which, according to our calculations, is expected to be approximately one order of magnitude higher than for the two larger core versions. The CL, calculated for seven rings of holes, is nearly two orders of magnitude higher in the 3c PBGF as compared to 7c (Fig. 3, mid row); it is worth pointing out that the latter could be reduced by approximately an order of magnitude by adding an extra ring of holes. An equally important attenuation mechanism in real PBGFs is the scattering from surface roughness at the core boundary interface, which can be shown to be proportional to the F-factor . The latter loss contribution is expected to increase with decreasing core size, and indeed our calculated values of F (Fig. 3, bottom row) suggest that the truly single mode guidance in fiber 3c is achieved at a penalty of a loss increase of 4–5 times as compared to a 7c, while the 7c is approximately 3–4 times as lossy as the 19c.
The transmission of the fabricated 3c PBGF is shown in Fig. 4. The fiber exhibits a ≈300 nm wide transmission window centered at approximately 1500 nm. The short wavelength edge is very sharp, as generally observed in 7c and 19c PBGFs, however the long wavelength edge is significantly less steep, which correlates well with the numerical results and in particular with the dispersion curve of the effective index and the confinement loss in Fig. 3. Despite the careful choice of elements in the initial stacked preform, resulting in an average core boundary thickness of about half the thickness of the struts in the photonic crystal cladding, our fiber exhibits a surface mode located close to the short wavelength bandgap edge (1415nm). We believe the presence of the SM is due to small scale deviations from the ideal design in the present fiber , which could be possible to eliminate by carefully controlling the pressure inside the hollow core during the fiber draw. The SM increases the overall transmission loss and reduces the available bandwidth to about 200nm (relative bandwidth ≈12%) for a 10m length. A minimum transmission loss of approximately 180dB/km was measured by the cutback method using a white light source (Fig. 4, insert). We believe that this value is determined by the surface mode and by fabrication-related factors in our fiber. However, based on the relative values of F-factor and on the lowest loss values reported for a 7c PBGF (13 dB/km at 1500nm  and 9.5dB/m at 1600nm ), we estimate that it should be possible to reduce the loss of a 3c PBGF to about 60dB/km at 1500nm and 40dB/km at 1600nm, respectively. We also investigated the bend loss of the 3c PBGF and found that the latter is substantially negligible even for tight bends (≤10mm radii), as previously reported for 7c and 19c PBGFs .
The modal properties of the 3c PBGF were investigated by recording the near-field mode profiles at 1540nm using a phosphor-coated silicon CCD camera. A variety of sample lengths and launch conditions were examined. The first column in Fig. 5 shows the linear intensity profiles of the fundamental air-guided modes of the 3c, 7c and 19c PBGFs, respectively, obtained under optimized launch conditions (obtained by butt-coupling the PBGF to a conventional single mode fiber) and by using relatively long fiber lengths. The 3c PBGF, however, exhibits robust single mode guidance (Fig. 5, top row) even in short (≈meter) lengths of fiber and when non-optimized coupling was employed. This was done by using a small focused spot (2.5µm), large NA (≈0.5) and by offsetting the fiber position at launch (see Fig. 5 for details). In particular, the effect of a spatial offset in the launch conditions for the 3c PBGF is only to reduce the coupling efficiency to the fundamental mode. The same behavior was observed at all other wavelengths within the low-loss transmission window of the 3c PBGF covered by the light source employed in our measurements (1525–1570nm). In contrast, the presence of higher order modes was very noticeable after a 5m length of the 7c fiber (Fig. 5, mid row) and after 50m length of the 19c fiber (bottom row). Offset launch conditions result in higher order modes being readily excited in the larger core structures and a significant fraction of the power can be coupled into such modes. It is worth noting that, although the fibers presented in this study are free of surface modes at the measurement wavelength (1540nm), a small fraction of the optical field resides in the silica core boundary, giving rise to 6, 12 and 18 satellite peaks in the 3c, 7c and 19c PBGFs respectively, which correlates very closely with the calculated modal profiles shown in Fig. 2. These peaks are comparatively stronger in fibers 3c and 7c, while in the 19c PBGF they are much less intense and are not completely resolved in our profiles.
For several of the most established practical applications of PBGFs (for instance as miniaturized gas cells ), the ability to make low-loss splices to conventional SMF fiber pigtails is paramount. This not only enables stable and efficient input and output coupling to the PBGF, but it also prevents the slow degradation of endfaces which is often observed when PBGFs are exposed to open atmosphere. Using an arc fusion splicer, we have been able to consistently obtain splices with a good mechanical strength and a total loss of ≈1.5–2dB (at 1550nm) for the 3c fiber, which compares to ≈1dB typical for 7c PBGFs. A moderate increase of the splicing loss is expected for the 3c PBGF, given that the effective area calculated for our fiber (27µm2) is significantly smaller than a standard SMF at 1550nm. This could be reduced, if required, by using a fiber with closer mode matching to the 3c PBGF, for instance a highly nonlinear fiber or a tapered SMF.
We have fabricated, for the first time to our knowledge, a novel type of air guiding photonic bandgap fiber that only supports a single degenerate pair of optical modes. The fiber is based on a triangular lattice of holes with a hollow core composed of just three omitted cells at its centre. The 3 cell PBGF exhibits robust, broadband single mode guidance as opposed to the more conventional PBGF structures, based on 7 cells and 19 cells cores. The transmission properties were both experimentally and numerically investigated and compared to those of 7 and 19 cell PBGFs. More pronounced wavelength dependence of all the main optical properties is found for the 3 cell PBGF, and the smaller core dimension correlates with marginally higher scattering losses but also with higher optical nonlinearity. We suggest that such moderate loss increase is compatible with application areas requiring relatively short device lengths and in which the single mode guidance may provide a definite advantage over the structures with larger cores. These include power delivery, interferometric and grating-based sensing, and nonlinear compression of ultrashort pulses.
References and links
1. P. Roberts, F. Couny, H. Sabert, B. Mangan, D. Williams, L. Farr, M. Mason, A. Tomlinson, T. Birks, J. Knight, and P. St. J. Russell, “Ultimate low loss of hollow-core photonic crystal fibres,” Opt. Express 13, 236–244 (2005) http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-1-236. [CrossRef] [PubMed]
2. L. F. Michaille, D. M. Taylor, C. R. H. Bennett, T. J. Shepherd, C. Jacobsen, and T. P. Hansen, “Damage threshold and bending properties of photonic crystal and photonic band-gap optical fibers,” Proc. SPIE 5618, 30–38 (2004). [CrossRef]
3. D. G. Ouzounov, F. R. Ahmad, D. Muller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, “Generation of megawatt optical solitons in hollow-core photonic band-gap fibers,” Science 301, 1702–1704 (2003). [CrossRef] [PubMed]
4. T. Ritari, J. Tuominen, H. Ludvigsen, J. Petersen, T. Sørensen, T. Hansen, and H. Simonsen, “Gas sensing using air-guiding photonic bandgap fibers,” Opt. Express 12, 4080–4087 (2004) http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-17-4080. [CrossRef] [PubMed]
5. F. Benabid, “Hollow-core photonic bandgap fibre: new light guidance for new science and technology,” Phil. Trans. R. Soc. A364, 3439–3462 (2006).
6. C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica-air photonic bandgap fiber,” Nature 424, 657–659 (2003). [CrossRef] [PubMed]
7. R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, “Single-mode photonic band gap guidance of light in air,” Science 285, 1537–1539 (1999). [CrossRef] [PubMed]
8. D. C. Allan, N. F. Borrelli, M. T. Gallagher, D. Müller, C. M. Smith, N. Venkataraman, J. A. West, P. Zhang, and K. W. Koch, “Surface modes and loss in air-core photonic bandgap fibers,” Proc. SPIE 5000, 161–174 (2003). [CrossRef]
9. J. West, C. Smith, N. Borrelli, D. Allan, and K. Koch, “Surface modes in air-core photonic band-gap fibers,” Opt. Express 12, 1485–1496 (2004) http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-8-1485. [CrossRef] [PubMed]
10. R. Amezcua-Correa, N. G. Broderick, M. N. Petrovich, F. Poletti, and D. J. Richardson, “Optimizing the usable bandwidth and loss through core design in realistic hollow-core photonic bandgap fibers,” Opt. Express 14, 7974–7985 (2006) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-14-17-7974. [CrossRef] [PubMed]
11. R. Amezcua-Correa, F. Gèrôme, S. G. Leon-Saval, N. G. R. Broderick, T. A. Birks, and J. C. Knight, “Control of surface modes in low loss hollow-core photonic bandgap fibers,” Opt. Express 16, 1142–1149 (2008) http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-2-1142. [CrossRef] [PubMed]
12. R. Amezcua-Correa, N. G. Broderick, M. N. Petrovich, F. Poletti, and D. J. Richardson, “Design of 7 and 19 cell core air-guiding photonic crystal fibers for low-loss wide bandwidth and dispersion controlled operation,” Opt. Express 15, 17577–17586 (2007) http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-26-17577. [CrossRef] [PubMed]
13. M. J. F. Digonnet, H. K. Kim, G. S. Kino, and S. Fan, “Understanding air-core photonic-bandgap fibers: analogy to conventional fibers,” J. Lightwave Technol. 23, 4169–4177 (2005) http://www.opticsinfobase.org/abstract.cfm?URI=JLT-23-12-4169 [CrossRef]
14. H. K. Kim, J. Shin, S. Fan, M. J. F. Digonnet, and G. S. Kino, “Designing air-core photonic-bandgap fibers free of surface modes,” IEEE J. of Quant. Electron. 40, 551–556 (2004). [CrossRef]
15. T. Murao, K. Saitoh, and M. Koshiba, “Realization of single-moded broadband air-guiding photonic bandgap fibers,” IEEE Photon. Technol. Lett. 18, 1666–1668 (2006). [CrossRef]
16. M. Wegmuller, M. Legré, N. Gisin, T. Hansen, C. Jakobsen, and J. Broeng, “Experimental investigation of the polarization properties of a hollow core photonic bandgap fiber for 1550 nm,” Opt. Express 13, 1457–1467 (2005) http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-5-1457. [CrossRef] [PubMed]
17. J. D. Shephard, P. J. Roberts, J. D. C. Jones, J. C. Knight, and D. P. Hand, “Measuring beam quality of hollow core photonic crystal fibers,” J. Lightwave Technol. 24, 3761–3769 (2006) http://www.opticsinfobase.org/abstract.cfm?URI=JLT-24-10-3761. [CrossRef]
18. S. Lebrun, P. Delaye, R. Frey, and G. Roosen, “High-efficiency single-mode Raman generation in a liquid-filled photonic bandgap fiber,” Opt. Lett. 32, 337–339 (2007) http://www.opticsinfobase.org/abstract.cfm?URI=ol-32-4-337. [CrossRef] [PubMed]
19. S. Blin, H. K. Kim, M. J. F. Digonnet, and G. S. Kino, “Reduced thermal sensitivity of a fiber-optic gyroscope using an air-core photonic-bandgap fiber,” J. Lightwave Technol. 25, 861–865 (2007) http://www.opticsinfobase.org/abstract.cfm?URI=JLT-25-3-861. [CrossRef]
20. N. A. Mortensen and M. D. Nielsen, “Modeling of realistic cladding structures for air-core photonic bandgap fibers,” Opt. Lett. 29, 349–351 (2004) http://www.opticsinfobase.org/abstract.cfm?URI=ol-29-4-349. [CrossRef] [PubMed]
21. F. Poletti, V. Finazzi, T. M. Monro, N. G. R. Broderick, V. Tse, and D. J. Richardson, “Inverse design and fabrication tolerances of ultra-flattened dispersion holey fibers,” Opt. Express 13, 3728–3736 (2005) http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-10-3728. [CrossRef] [PubMed]
22. K. Saitoh and M. Koshiba, “Leakage loss and group velocity dispersion in air-core photonic bandgap fibers,” Opt. Express 11, 3100–3109 (2003) http://www.opticsinfobase.org/abstract.cfm?URI=oe-11-23-3100. [CrossRef] [PubMed]
23. F. Poletti, N. G. Broderick, D. Richardson, and T. Monro, “The effect of core asymmetries on the polarization properties of hollow core photonic bandgap fibers,” Opt. Express 13, 9115–9124 (2005) http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-22-9115. [CrossRef] [PubMed]
24. T. P. Hansen, J. Broeng, C. Jakobsen, G. Vienne, H. R. Simonsen, M. D. Nielsen, P. M. W. Skovgaard, J. R. Folkenberg, and A. Bjarklev, “Air-Guiding Photonic Bandgap Fibers: Spectral Properties, Macrobending Loss, and Practical Handling,” J. Lightwave Technol. 22, 11–15 (2004) http://www.opticsinfobase.org/abstract.cfm?URI=JLT-22-1-11. [CrossRef]
25. F. Benabid, F. Couny, J. C. Knight, T. A. Birks, and P. St J. Russell, “Compact, stable and efficient all-fibre gas cells using hollow-core photonic crystal fibres,” Nature 434, 488–491 (2005). [CrossRef] [PubMed]